The present invention relates to methods for determining stress parameters from sonic velocity measurements in an earth formation around a borehole.
Formation stresses play an important role in geophysical prospecting and development of oil and gas reservoirs. Knowledge of both the direction and magnitude of these stresses is required to ensure borehole stability during directional drilling, to facilitate hydraulic fracturing for enhanced production, and to facilitate selective perforation for prevention of sanding during production. A detailed knowledge of formation stresses also helps producers manage reservoirs that are prone to subsidence caused by a significant reduction in pore fluid pressure (herein referred to asxe2x80x9cpore pressurexe2x80x9d) and an associated increase in the effective stress that exceeds the in-situ rock strength.
The formation stress state is characterized by the magnitude and direction of the three principal stresses. Generally, the overburden stress yields the principal stress in the vertical direction. The overburden stress (SV) is reliably obtained by integrating the formation mass density from the surface to the depth of interest. Accordingly, to fully characterize the formation stress state, it is necessary to determine the two principal stresses in the horizontal plane maximum and minimum horizontal stresses, SH max and Sh min, respectively.
Existing techniques for estimating the maximum and minimum horizontal stresses are based on analyzing borehole breakouts and borehole pressure necessary to fracture the surrounding formation, respectively. Both borehole break-outs and hydraulic fracturing are destructive techniques that rely on assumed failure models. For example, a borehole breakout analysis can be used only in the presence of a compressive-shear failure and assumed cohesive strength and friction angle in the Mohr-Coulomb failure envelope (Gough and Bell, 1982; Zoback et al., 1985). The hydraulic fracturing technique for the estimation of SH max requires a reliable knowledge of the rock in-situ tensile strength that is difficult to obtain.
Hydraulic Fracturing and Wellbore Breakouts
The standard technique for determining in-situ formation stresses is based on hydraulic fracturing of surrounding formation between a sealed-off interval in a borehole. The technique includes applying increasing hydraulic pressure in the sealed-off interval to produce a radial fracture. The rock fractures when the circumferential stress produced by pressure and borehole-induced stress concentrations exceeds the tensile strength of rock. The effective circumferential (or hoop) stress at the borehole surface for an elastic deformation of a nonporous and impermeable formation is given by (Vernik and Zoback, 1992)
"sgr"xcex8xcex8=(SH max+Sh min)-2 COS 2xcex8(SH maxxe2x88x92Sh min)xe2x88x92Pw,xe2x80x83xe2x80x83(1)
where xcex8 is the angle measured from the SH max direction; and PW is the wellbore pressure. Hydraulic fracturing applies a tensile failure model at xcex8=0xc2x0 and 180xc2x0, and wellbore breakouts uses a compressive-shear failure model at xcex8=90xc2x0 and 270xc2x0 for the estimation of maximum and minimum horizontal stresses in the far-field. Hubbert and Willis proposed that if Pb were the breakdown or fracture pressure in the borehole, the relationship between the maximum and minimum horizontal stresses is given by
SH max=3Sh minxe2x88x92Pb xe2x88x92Pp+To,xe2x80x83xe2x80x83(2)
where To is the tensile strength at the borehole surface, PP is the formation pore pressure, and it is assumed that there is no fluid injection into the formation. This expression yields an upper bound on the breakdown pressure. If fluid injection occurs (i.e. mud penetrates the formation), there is a reduction in the breakdown pressure magnitude. In the presence of any plastic deformation at the borehole surface or borehole wall cooling during drilling (Moos and Zoback, 1990), the hoop stress at the borehole surface is appreciably reduced and this results in an overestimate of the maximum horizontal stress SH max magnitude.
Minimum horizontal stress Sh min can be determined more reliably using hydraulic fracturing and a method proposed by Roegiers. After the fracture has propagated for a while, the hydraulic pumps are stopped and an instantaneous shut-in pressure is recorded. This pressure is only slightly above the minimum principal stressxe2x80x94assuming the influence of borehole to be negligibly small. Therefore, the instantaneous shut-in pressure is taken to be the minimum horizontal stress Sh min (Roegiers, 1989).
After the formation has bled off, a second cycle of pressurization is started with the same pressurizing fluid and the same pumping rate as the first cycle. The pressure required to re-open the fractures, Preopen is recorded and subtracted from the breakdown pressure Pb, to yield the tensile strength To. However, estimation of the tensile strength is not very reliable.
Vernik and Zoback (1992) have shown from core analysis that there is a significant tensile and compressive strength anisotropy in rocks. They have suggested the use of an effective strength in the failure model used in the estimation of the maximum horizontal stress SH max magnitude from the wellbore breakout analysis. The SH max can be estimated from the following equation                                           S                          H              ⁢                              xe2x80x83                            ⁢              max                                =                                                                      C                  ef                                +                                  P                  w                                                            1                -                                  2                  ⁢                  cos                  ⁢                                      xe2x80x83                                    ⁢                                      (                                          π                      -                                              2                        ⁢                                                  φ                          b                                                                                      )                                                                        -                                          S                                  h                  ⁢                                      xe2x80x83                                    ⁢                  min                                            ⁢                              xe2x80x83                            ⁢                                                1                  +                                      2                    ⁢                    cos                    ⁢                                          xe2x80x83                                        ⁢                                          (                                              π                        -                                                  2                          ⁢                                                      φ                            b                                                                                              )                                                                                        1                  -                                      2                    ⁢                    cos                    ⁢                                          xe2x80x83                                        ⁢                                          (                                              π                        -                                                  2                          ⁢                                                      φ                            b                                                                                              )                                                                                                          ,                            (        3        )            
where 2xcfx86b is the breakout width, and PW is the wellbore pressure. This equation is derived from the effective stress with 2xcex8=xcfx80/2xe2x88x92xcfx86b, and Cef is the effective compressive strength of the formation near the borehole surface.
Pore Pressure in Over-Pressured Formations
Existing techniques for determining pore pressure in an overpressured formation attempt to account for the potential source of pore pressure increase in terms of undercompaction (resulting in an increase in porosity) and/or pore fluid expansion caused by a variety of geological processes (Eaton, 1975; Bowers, 1994). Eaton (1975) proposed an empirical relationship between the measured compressional velocity V and the effective stress "sgr"
V=Vo+C"sgr"⅓xe2x80x83xe2x80x83(4)
where the empirical parameter C is obtained by fitting the velocity-effective stress data in a normally compacted zone. Below the top of overpressure in the velocity reversal zone, using the same empirical parameter C and the exponent ⅓ may lead to an underestimate of the pore pressure increase. Bower (U.S. Pat. No. 5,200,929, Apr. 6, 1993) has proposed to remedy the limitation of the Eaton""s technique by assuming two different empirical relations between the measured compressional velocity and effective stress. These two different relations in a normally compacted and velocity-reversal zones are constructed to account for the undercompaction and pore-fluid expansion (that may be caused by temperature changes, hydrocarbon maturation, and clay diagenesis). Bower (SPE 27488, 1994) has proposed the following relationship between the measured compressional velocity and effective stress a in a normally compacted zone (also referred to as the virgin curve)
V=Vo+A"sgr"Bxe2x80x83xe2x80x83(5)
where Vo is the velocity at the beginning of the normal compaction zone; A and B are the empirical parameters obtained from velocity-effective stress data in a nearby offset well. The velocity-effective stress in a velocity-reversal zone attributable to a fluid-expansion effect and an associated hysteretic response is described by
V=Vo+A["sgr"MAX("sgr"/"sgr"MAX)1/U]Bxe2x80x83xe2x80x83(6)
where A and B are the same as before, but U is a third parameter to be determined from the measured data in a nearby offset well. "sgr"MAX is defined by                               σ          MAX                =                              (                                                            V                  MAX                                -                                  V                  0                                            A                        )                                1            /            B                                              (        7        )            
where "sgr"MAX and VMAX are estimates of the effective stress and velocity at the onset of unloading.
Both Eaton""s and Bowers""s techniques define the effective stress "sgr"=Svxe2x88x92Pp, where SV is the overburden stress, and PP is the pore pressure in both the normally compacted and overpressured zones (implying that the Biot parameter xcex1=0).
Existing techniques for the detection of overpressured (shale) formations include analyzing a formation resistivity, rate of (drill-bit) penetration, and compressional velocity logs that can be measured while drilling (Hottman and Johnson, 1965; Bowers, 1995). A rapid decrease in formation resistivity, a rapid increase in the rate of penetration, and a rapid decrease in the compressional velocity at a certain depth are indicators of the top of overpressured shale or formation. These indicators are useful for the driller for maintaining wellbore stability by a proper adjustment of the mud weight that avoids borehole breakouts or tensile fractions leading to a significant mud loss. There is a need in the industry for a reliable estimate of the magnitude of the pore pressure increase in the overpressured formation.
The present invention provides a method for determining an unknown stress parameter of an earth formation within a selected depth interval proximate to a borehole.
A first embodiment includes measuring a first set of parameters of the formation within a selected depth interval to produce a first set of measured values. The first set of parameters includes compressional velocity, fast-shear velocity, slow-shear velocity and Stoneley velocity. The first embodiment also includes estimating a second set of parameters of the formation to produce estimated values. It also includes solving a set of first, second, third, and fourth velocity difference equations by executing a least squares minimization program to determine the unknown stress parameter using the measured values and the estimated values. The first equation includes a compressional velocity term, the second equation includes a fast-shear velocity term, the third equation includes a slow-shear velocity term, and the fourth equation includes a Stoneley velocity term. The first embodiment also includes solving a fifth equation to determine to determine the specific unknown stress parameter at a given depth within the depth interval.
A first version of the first embodiment includes solving a fifth equation to determine total maximum horizontal stress at the given depth. In this version the fifth equation contains the Biot parameter to correct for porosity, pore shape and connectivity.
A second version of the first embodiment includes solving a fifth equation to determine total minimum horizontal stress at the given depth. In this version, as in the first version, the fifth equation includes the Biot parameter to correct for porosity, pore shape and connectivity.
A third version of the first embodiment includes solving a fifth equation to determine pore pressure gradient at the given depth. In this version the fifth equation includes dividing pore pressure difference across the selected depth interval by the depth of the depth interval.
A fourth version of the first embodiment determines minimum horizontal stress gradient by inversion of velocity difference equations using estimates of overburden stress, pore pressure, and maximum horizontal stress gradient.
A fifth version of the first embodiment determines pore pressure gradient by inversion of velocity difference equations using estimates of overburden stress, maximum horizontal stress gradient, and minimum horizontal stress gradient.
A second embodiment provides a method for determining the difference in pore pressure at a given depth in an earth formation proximate to a borehole, before and after a production period. The method of the second embodiment includes measuring a first set of parameters of the formation within a selected depth interval of the borehole before and after the production period to produce a first and second set of measured values, respectively. The set of parameters includes one velocity of a group of velocities, the group consisting of compressional velocity, fast-shear velocity and slow-shear velocity. The method of the second embodiment also includes estimating a second set of parameters of the formation to produce estimated values. It further includes solving at least one velocity difference equation to determine the unknown stress parameter at a depth within the depth interval using the first and second sets of measured values and the estimated values. It further includes solving another equation involving linear and non-linear stress coefficients to determine difference in pore pressure.
A first version of the second embodiment uses measured compressional velocity values.
A second version of the second embodiment uses measured fast-shear velocity values.
A third version of the second embodiment uses measured slow-shear velocity values.
A third embodiment provides a method for determining pore fluid overpressure in an overpressured shale formation.